<HTML>
<BODY BGCOLOR="white">
<PRE>
<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    <a name="line.17"></a>
<FONT color="green">018</FONT>    package org.apache.commons.math3.util;<a name="line.18"></a>
<FONT color="green">019</FONT>    <a name="line.19"></a>
<FONT color="green">020</FONT>    import java.math.BigDecimal;<a name="line.20"></a>
<FONT color="green">021</FONT>    <a name="line.21"></a>
<FONT color="green">022</FONT>    import org.apache.commons.math3.exception.MathArithmeticException;<a name="line.22"></a>
<FONT color="green">023</FONT>    import org.apache.commons.math3.exception.MathIllegalArgumentException;<a name="line.23"></a>
<FONT color="green">024</FONT>    import org.apache.commons.math3.exception.util.LocalizedFormats;<a name="line.24"></a>
<FONT color="green">025</FONT>    <a name="line.25"></a>
<FONT color="green">026</FONT>    /**<a name="line.26"></a>
<FONT color="green">027</FONT>     * Utilities for comparing numbers.<a name="line.27"></a>
<FONT color="green">028</FONT>     *<a name="line.28"></a>
<FONT color="green">029</FONT>     * @since 3.0<a name="line.29"></a>
<FONT color="green">030</FONT>     * @version $Id: Precision.java 1422313 2012-12-15 18:53:41Z psteitz $<a name="line.30"></a>
<FONT color="green">031</FONT>     */<a name="line.31"></a>
<FONT color="green">032</FONT>    public class Precision {<a name="line.32"></a>
<FONT color="green">033</FONT>        /**<a name="line.33"></a>
<FONT color="green">034</FONT>         * &lt;p&gt;<a name="line.34"></a>
<FONT color="green">035</FONT>         * Largest double-precision floating-point number such that<a name="line.35"></a>
<FONT color="green">036</FONT>         * {@code 1 + EPSILON} is numerically equal to 1. This value is an upper<a name="line.36"></a>
<FONT color="green">037</FONT>         * bound on the relative error due to rounding real numbers to double<a name="line.37"></a>
<FONT color="green">038</FONT>         * precision floating-point numbers.<a name="line.38"></a>
<FONT color="green">039</FONT>         * &lt;/p&gt;<a name="line.39"></a>
<FONT color="green">040</FONT>         * &lt;p&gt;<a name="line.40"></a>
<FONT color="green">041</FONT>         * In IEEE 754 arithmetic, this is 2&lt;sup&gt;-53&lt;/sup&gt;.<a name="line.41"></a>
<FONT color="green">042</FONT>         * &lt;/p&gt;<a name="line.42"></a>
<FONT color="green">043</FONT>         *<a name="line.43"></a>
<FONT color="green">044</FONT>         * @see &lt;a href="http://en.wikipedia.org/wiki/Machine_epsilon"&gt;Machine epsilon&lt;/a&gt;<a name="line.44"></a>
<FONT color="green">045</FONT>         */<a name="line.45"></a>
<FONT color="green">046</FONT>        public static final double EPSILON;<a name="line.46"></a>
<FONT color="green">047</FONT>    <a name="line.47"></a>
<FONT color="green">048</FONT>        /**<a name="line.48"></a>
<FONT color="green">049</FONT>         * Safe minimum, such that {@code 1 / SAFE_MIN} does not overflow.<a name="line.49"></a>
<FONT color="green">050</FONT>         * &lt;br/&gt;<a name="line.50"></a>
<FONT color="green">051</FONT>         * In IEEE 754 arithmetic, this is also the smallest normalized<a name="line.51"></a>
<FONT color="green">052</FONT>         * number 2&lt;sup&gt;-1022&lt;/sup&gt;.<a name="line.52"></a>
<FONT color="green">053</FONT>         */<a name="line.53"></a>
<FONT color="green">054</FONT>        public static final double SAFE_MIN;<a name="line.54"></a>
<FONT color="green">055</FONT>    <a name="line.55"></a>
<FONT color="green">056</FONT>        /** Exponent offset in IEEE754 representation. */<a name="line.56"></a>
<FONT color="green">057</FONT>        private static final long EXPONENT_OFFSET = 1023l;<a name="line.57"></a>
<FONT color="green">058</FONT>    <a name="line.58"></a>
<FONT color="green">059</FONT>        /** Offset to order signed double numbers lexicographically. */<a name="line.59"></a>
<FONT color="green">060</FONT>        private static final long SGN_MASK = 0x8000000000000000L;<a name="line.60"></a>
<FONT color="green">061</FONT>        /** Offset to order signed double numbers lexicographically. */<a name="line.61"></a>
<FONT color="green">062</FONT>        private static final int SGN_MASK_FLOAT = 0x80000000;<a name="line.62"></a>
<FONT color="green">063</FONT>    <a name="line.63"></a>
<FONT color="green">064</FONT>        static {<a name="line.64"></a>
<FONT color="green">065</FONT>            /*<a name="line.65"></a>
<FONT color="green">066</FONT>             *  This was previously expressed as = 0x1.0p-53;<a name="line.66"></a>
<FONT color="green">067</FONT>             *  However, OpenJDK (Sparc Solaris) cannot handle such small<a name="line.67"></a>
<FONT color="green">068</FONT>             *  constants: MATH-721<a name="line.68"></a>
<FONT color="green">069</FONT>             */<a name="line.69"></a>
<FONT color="green">070</FONT>            EPSILON = Double.longBitsToDouble((EXPONENT_OFFSET - 53l) &lt;&lt; 52);<a name="line.70"></a>
<FONT color="green">071</FONT>    <a name="line.71"></a>
<FONT color="green">072</FONT>            /*<a name="line.72"></a>
<FONT color="green">073</FONT>             * This was previously expressed as = 0x1.0p-1022;<a name="line.73"></a>
<FONT color="green">074</FONT>             * However, OpenJDK (Sparc Solaris) cannot handle such small<a name="line.74"></a>
<FONT color="green">075</FONT>             * constants: MATH-721<a name="line.75"></a>
<FONT color="green">076</FONT>             */<a name="line.76"></a>
<FONT color="green">077</FONT>            SAFE_MIN = Double.longBitsToDouble((EXPONENT_OFFSET - 1022l) &lt;&lt; 52);<a name="line.77"></a>
<FONT color="green">078</FONT>        }<a name="line.78"></a>
<FONT color="green">079</FONT>    <a name="line.79"></a>
<FONT color="green">080</FONT>        /**<a name="line.80"></a>
<FONT color="green">081</FONT>         * Private constructor.<a name="line.81"></a>
<FONT color="green">082</FONT>         */<a name="line.82"></a>
<FONT color="green">083</FONT>        private Precision() {}<a name="line.83"></a>
<FONT color="green">084</FONT>    <a name="line.84"></a>
<FONT color="green">085</FONT>        /**<a name="line.85"></a>
<FONT color="green">086</FONT>         * Compares two numbers given some amount of allowed error.<a name="line.86"></a>
<FONT color="green">087</FONT>         *<a name="line.87"></a>
<FONT color="green">088</FONT>         * @param x the first number<a name="line.88"></a>
<FONT color="green">089</FONT>         * @param y the second number<a name="line.89"></a>
<FONT color="green">090</FONT>         * @param eps the amount of error to allow when checking for equality<a name="line.90"></a>
<FONT color="green">091</FONT>         * @return &lt;ul&gt;&lt;li&gt;0 if  {@link #equals(double, double, double) equals(x, y, eps)}&lt;/li&gt;<a name="line.91"></a>
<FONT color="green">092</FONT>         *       &lt;li&gt;&amp;lt; 0 if !{@link #equals(double, double, double) equals(x, y, eps)} &amp;amp;&amp;amp; x &amp;lt; y&lt;/li&gt;<a name="line.92"></a>
<FONT color="green">093</FONT>         *       &lt;li&gt;&gt; 0 if !{@link #equals(double, double, double) equals(x, y, eps)} &amp;amp;&amp;amp; x &gt; y&lt;/li&gt;&lt;/ul&gt;<a name="line.93"></a>
<FONT color="green">094</FONT>         */<a name="line.94"></a>
<FONT color="green">095</FONT>        public static int compareTo(double x, double y, double eps) {<a name="line.95"></a>
<FONT color="green">096</FONT>            if (equals(x, y, eps)) {<a name="line.96"></a>
<FONT color="green">097</FONT>                return 0;<a name="line.97"></a>
<FONT color="green">098</FONT>            } else if (x &lt; y) {<a name="line.98"></a>
<FONT color="green">099</FONT>                return -1;<a name="line.99"></a>
<FONT color="green">100</FONT>            }<a name="line.100"></a>
<FONT color="green">101</FONT>            return 1;<a name="line.101"></a>
<FONT color="green">102</FONT>        }<a name="line.102"></a>
<FONT color="green">103</FONT>    <a name="line.103"></a>
<FONT color="green">104</FONT>        /**<a name="line.104"></a>
<FONT color="green">105</FONT>         * Compares two numbers given some amount of allowed error.<a name="line.105"></a>
<FONT color="green">106</FONT>         * Two float numbers are considered equal if there are {@code (maxUlps - 1)}<a name="line.106"></a>
<FONT color="green">107</FONT>         * (or fewer) floating point numbers between them, i.e. two adjacent floating<a name="line.107"></a>
<FONT color="green">108</FONT>         * point numbers are considered equal.<a name="line.108"></a>
<FONT color="green">109</FONT>         * Adapted from &lt;a<a name="line.109"></a>
<FONT color="green">110</FONT>         * href="http://www.cygnus-software.com/papers/comparingfloats/comparingfloats.htm"&gt;<a name="line.110"></a>
<FONT color="green">111</FONT>         * Bruce Dawson&lt;/a&gt;<a name="line.111"></a>
<FONT color="green">112</FONT>         *<a name="line.112"></a>
<FONT color="green">113</FONT>         * @param x first value<a name="line.113"></a>
<FONT color="green">114</FONT>         * @param y second value<a name="line.114"></a>
<FONT color="green">115</FONT>         * @param maxUlps {@code (maxUlps - 1)} is the number of floating point<a name="line.115"></a>
<FONT color="green">116</FONT>         * values between {@code x} and {@code y}.<a name="line.116"></a>
<FONT color="green">117</FONT>         * @return &lt;ul&gt;&lt;li&gt;0 if  {@link #equals(double, double, int) equals(x, y, maxUlps)}&lt;/li&gt;<a name="line.117"></a>
<FONT color="green">118</FONT>         *       &lt;li&gt;&amp;lt; 0 if !{@link #equals(double, double, int) equals(x, y, maxUlps)} &amp;amp;&amp;amp; x &amp;lt; y&lt;/li&gt;<a name="line.118"></a>
<FONT color="green">119</FONT>         *       &lt;li&gt;&gt; 0 if !{@link #equals(double, double, int) equals(x, y, maxUlps)} &amp;amp;&amp;amp; x &gt; y&lt;/li&gt;&lt;/ul&gt;<a name="line.119"></a>
<FONT color="green">120</FONT>         */<a name="line.120"></a>
<FONT color="green">121</FONT>        public static int compareTo(final double x, final double y, final int maxUlps) {<a name="line.121"></a>
<FONT color="green">122</FONT>            if (equals(x, y, maxUlps)) {<a name="line.122"></a>
<FONT color="green">123</FONT>                return 0;<a name="line.123"></a>
<FONT color="green">124</FONT>            } else if (x &lt; y) {<a name="line.124"></a>
<FONT color="green">125</FONT>                return -1;<a name="line.125"></a>
<FONT color="green">126</FONT>            }<a name="line.126"></a>
<FONT color="green">127</FONT>            return 1;<a name="line.127"></a>
<FONT color="green">128</FONT>        }<a name="line.128"></a>
<FONT color="green">129</FONT>    <a name="line.129"></a>
<FONT color="green">130</FONT>        /**<a name="line.130"></a>
<FONT color="green">131</FONT>         * Returns true iff they are equal as defined by<a name="line.131"></a>
<FONT color="green">132</FONT>         * {@link #equals(float,float,int) equals(x, y, 1)}.<a name="line.132"></a>
<FONT color="green">133</FONT>         *<a name="line.133"></a>
<FONT color="green">134</FONT>         * @param x first value<a name="line.134"></a>
<FONT color="green">135</FONT>         * @param y second value<a name="line.135"></a>
<FONT color="green">136</FONT>         * @return {@code true} if the values are equal.<a name="line.136"></a>
<FONT color="green">137</FONT>         */<a name="line.137"></a>
<FONT color="green">138</FONT>        public static boolean equals(float x, float y) {<a name="line.138"></a>
<FONT color="green">139</FONT>            return equals(x, y, 1);<a name="line.139"></a>
<FONT color="green">140</FONT>        }<a name="line.140"></a>
<FONT color="green">141</FONT>    <a name="line.141"></a>
<FONT color="green">142</FONT>        /**<a name="line.142"></a>
<FONT color="green">143</FONT>         * Returns true if both arguments are NaN or neither is NaN and they are<a name="line.143"></a>
<FONT color="green">144</FONT>         * equal as defined by {@link #equals(float,float) equals(x, y, 1)}.<a name="line.144"></a>
<FONT color="green">145</FONT>         *<a name="line.145"></a>
<FONT color="green">146</FONT>         * @param x first value<a name="line.146"></a>
<FONT color="green">147</FONT>         * @param y second value<a name="line.147"></a>
<FONT color="green">148</FONT>         * @return {@code true} if the values are equal or both are NaN.<a name="line.148"></a>
<FONT color="green">149</FONT>         * @since 2.2<a name="line.149"></a>
<FONT color="green">150</FONT>         */<a name="line.150"></a>
<FONT color="green">151</FONT>        public static boolean equalsIncludingNaN(float x, float y) {<a name="line.151"></a>
<FONT color="green">152</FONT>            return (Float.isNaN(x) &amp;&amp; Float.isNaN(y)) || equals(x, y, 1);<a name="line.152"></a>
<FONT color="green">153</FONT>        }<a name="line.153"></a>
<FONT color="green">154</FONT>    <a name="line.154"></a>
<FONT color="green">155</FONT>        /**<a name="line.155"></a>
<FONT color="green">156</FONT>         * Returns true if both arguments are equal or within the range of allowed<a name="line.156"></a>
<FONT color="green">157</FONT>         * error (inclusive).<a name="line.157"></a>
<FONT color="green">158</FONT>         *<a name="line.158"></a>
<FONT color="green">159</FONT>         * @param x first value<a name="line.159"></a>
<FONT color="green">160</FONT>         * @param y second value<a name="line.160"></a>
<FONT color="green">161</FONT>         * @param eps the amount of absolute error to allow.<a name="line.161"></a>
<FONT color="green">162</FONT>         * @return {@code true} if the values are equal or within range of each other.<a name="line.162"></a>
<FONT color="green">163</FONT>         * @since 2.2<a name="line.163"></a>
<FONT color="green">164</FONT>         */<a name="line.164"></a>
<FONT color="green">165</FONT>        public static boolean equals(float x, float y, float eps) {<a name="line.165"></a>
<FONT color="green">166</FONT>            return equals(x, y, 1) || FastMath.abs(y - x) &lt;= eps;<a name="line.166"></a>
<FONT color="green">167</FONT>        }<a name="line.167"></a>
<FONT color="green">168</FONT>    <a name="line.168"></a>
<FONT color="green">169</FONT>        /**<a name="line.169"></a>
<FONT color="green">170</FONT>         * Returns true if both arguments are NaN or are equal or within the range<a name="line.170"></a>
<FONT color="green">171</FONT>         * of allowed error (inclusive).<a name="line.171"></a>
<FONT color="green">172</FONT>         *<a name="line.172"></a>
<FONT color="green">173</FONT>         * @param x first value<a name="line.173"></a>
<FONT color="green">174</FONT>         * @param y second value<a name="line.174"></a>
<FONT color="green">175</FONT>         * @param eps the amount of absolute error to allow.<a name="line.175"></a>
<FONT color="green">176</FONT>         * @return {@code true} if the values are equal or within range of each other,<a name="line.176"></a>
<FONT color="green">177</FONT>         * or both are NaN.<a name="line.177"></a>
<FONT color="green">178</FONT>         * @since 2.2<a name="line.178"></a>
<FONT color="green">179</FONT>         */<a name="line.179"></a>
<FONT color="green">180</FONT>        public static boolean equalsIncludingNaN(float x, float y, float eps) {<a name="line.180"></a>
<FONT color="green">181</FONT>            return equalsIncludingNaN(x, y) || (FastMath.abs(y - x) &lt;= eps);<a name="line.181"></a>
<FONT color="green">182</FONT>        }<a name="line.182"></a>
<FONT color="green">183</FONT>    <a name="line.183"></a>
<FONT color="green">184</FONT>        /**<a name="line.184"></a>
<FONT color="green">185</FONT>         * Returns true if both arguments are equal or within the range of allowed<a name="line.185"></a>
<FONT color="green">186</FONT>         * error (inclusive).<a name="line.186"></a>
<FONT color="green">187</FONT>         * Two float numbers are considered equal if there are {@code (maxUlps - 1)}<a name="line.187"></a>
<FONT color="green">188</FONT>         * (or fewer) floating point numbers between them, i.e. two adjacent floating<a name="line.188"></a>
<FONT color="green">189</FONT>         * point numbers are considered equal.<a name="line.189"></a>
<FONT color="green">190</FONT>         * Adapted from &lt;a<a name="line.190"></a>
<FONT color="green">191</FONT>         * href="http://www.cygnus-software.com/papers/comparingfloats/comparingfloats.htm"&gt;<a name="line.191"></a>
<FONT color="green">192</FONT>         * Bruce Dawson&lt;/a&gt;<a name="line.192"></a>
<FONT color="green">193</FONT>         *<a name="line.193"></a>
<FONT color="green">194</FONT>         * @param x first value<a name="line.194"></a>
<FONT color="green">195</FONT>         * @param y second value<a name="line.195"></a>
<FONT color="green">196</FONT>         * @param maxUlps {@code (maxUlps - 1)} is the number of floating point<a name="line.196"></a>
<FONT color="green">197</FONT>         * values between {@code x} and {@code y}.<a name="line.197"></a>
<FONT color="green">198</FONT>         * @return {@code true} if there are fewer than {@code maxUlps} floating<a name="line.198"></a>
<FONT color="green">199</FONT>         * point values between {@code x} and {@code y}.<a name="line.199"></a>
<FONT color="green">200</FONT>         * @since 2.2<a name="line.200"></a>
<FONT color="green">201</FONT>         */<a name="line.201"></a>
<FONT color="green">202</FONT>        public static boolean equals(float x, float y, int maxUlps) {<a name="line.202"></a>
<FONT color="green">203</FONT>            int xInt = Float.floatToIntBits(x);<a name="line.203"></a>
<FONT color="green">204</FONT>            int yInt = Float.floatToIntBits(y);<a name="line.204"></a>
<FONT color="green">205</FONT>    <a name="line.205"></a>
<FONT color="green">206</FONT>            // Make lexicographically ordered as a two's-complement integer.<a name="line.206"></a>
<FONT color="green">207</FONT>            if (xInt &lt; 0) {<a name="line.207"></a>
<FONT color="green">208</FONT>                xInt = SGN_MASK_FLOAT - xInt;<a name="line.208"></a>
<FONT color="green">209</FONT>            }<a name="line.209"></a>
<FONT color="green">210</FONT>            if (yInt &lt; 0) {<a name="line.210"></a>
<FONT color="green">211</FONT>                yInt = SGN_MASK_FLOAT - yInt;<a name="line.211"></a>
<FONT color="green">212</FONT>            }<a name="line.212"></a>
<FONT color="green">213</FONT>    <a name="line.213"></a>
<FONT color="green">214</FONT>            final boolean isEqual = FastMath.abs(xInt - yInt) &lt;= maxUlps;<a name="line.214"></a>
<FONT color="green">215</FONT>    <a name="line.215"></a>
<FONT color="green">216</FONT>            return isEqual &amp;&amp; !Float.isNaN(x) &amp;&amp; !Float.isNaN(y);<a name="line.216"></a>
<FONT color="green">217</FONT>        }<a name="line.217"></a>
<FONT color="green">218</FONT>    <a name="line.218"></a>
<FONT color="green">219</FONT>        /**<a name="line.219"></a>
<FONT color="green">220</FONT>         * Returns true if both arguments are NaN or if they are equal as defined<a name="line.220"></a>
<FONT color="green">221</FONT>         * by {@link #equals(float,float,int) equals(x, y, maxUlps)}.<a name="line.221"></a>
<FONT color="green">222</FONT>         *<a name="line.222"></a>
<FONT color="green">223</FONT>         * @param x first value<a name="line.223"></a>
<FONT color="green">224</FONT>         * @param y second value<a name="line.224"></a>
<FONT color="green">225</FONT>         * @param maxUlps {@code (maxUlps - 1)} is the number of floating point<a name="line.225"></a>
<FONT color="green">226</FONT>         * values between {@code x} and {@code y}.<a name="line.226"></a>
<FONT color="green">227</FONT>         * @return {@code true} if both arguments are NaN or if there are less than<a name="line.227"></a>
<FONT color="green">228</FONT>         * {@code maxUlps} floating point values between {@code x} and {@code y}.<a name="line.228"></a>
<FONT color="green">229</FONT>         * @since 2.2<a name="line.229"></a>
<FONT color="green">230</FONT>         */<a name="line.230"></a>
<FONT color="green">231</FONT>        public static boolean equalsIncludingNaN(float x, float y, int maxUlps) {<a name="line.231"></a>
<FONT color="green">232</FONT>            return (Float.isNaN(x) &amp;&amp; Float.isNaN(y)) || equals(x, y, maxUlps);<a name="line.232"></a>
<FONT color="green">233</FONT>        }<a name="line.233"></a>
<FONT color="green">234</FONT>    <a name="line.234"></a>
<FONT color="green">235</FONT>        /**<a name="line.235"></a>
<FONT color="green">236</FONT>         * Returns true iff they are equal as defined by<a name="line.236"></a>
<FONT color="green">237</FONT>         * {@link #equals(double,double,int) equals(x, y, 1)}.<a name="line.237"></a>
<FONT color="green">238</FONT>         *<a name="line.238"></a>
<FONT color="green">239</FONT>         * @param x first value<a name="line.239"></a>
<FONT color="green">240</FONT>         * @param y second value<a name="line.240"></a>
<FONT color="green">241</FONT>         * @return {@code true} if the values are equal.<a name="line.241"></a>
<FONT color="green">242</FONT>         */<a name="line.242"></a>
<FONT color="green">243</FONT>        public static boolean equals(double x, double y) {<a name="line.243"></a>
<FONT color="green">244</FONT>            return equals(x, y, 1);<a name="line.244"></a>
<FONT color="green">245</FONT>        }<a name="line.245"></a>
<FONT color="green">246</FONT>    <a name="line.246"></a>
<FONT color="green">247</FONT>        /**<a name="line.247"></a>
<FONT color="green">248</FONT>         * Returns true if both arguments are NaN or neither is NaN and they are<a name="line.248"></a>
<FONT color="green">249</FONT>         * equal as defined by {@link #equals(double,double) equals(x, y, 1)}.<a name="line.249"></a>
<FONT color="green">250</FONT>         *<a name="line.250"></a>
<FONT color="green">251</FONT>         * @param x first value<a name="line.251"></a>
<FONT color="green">252</FONT>         * @param y second value<a name="line.252"></a>
<FONT color="green">253</FONT>         * @return {@code true} if the values are equal or both are NaN.<a name="line.253"></a>
<FONT color="green">254</FONT>         * @since 2.2<a name="line.254"></a>
<FONT color="green">255</FONT>         */<a name="line.255"></a>
<FONT color="green">256</FONT>        public static boolean equalsIncludingNaN(double x, double y) {<a name="line.256"></a>
<FONT color="green">257</FONT>            return (Double.isNaN(x) &amp;&amp; Double.isNaN(y)) || equals(x, y, 1);<a name="line.257"></a>
<FONT color="green">258</FONT>        }<a name="line.258"></a>
<FONT color="green">259</FONT>    <a name="line.259"></a>
<FONT color="green">260</FONT>        /**<a name="line.260"></a>
<FONT color="green">261</FONT>         * Returns {@code true} if there is no double value strictly between the<a name="line.261"></a>
<FONT color="green">262</FONT>         * arguments or the difference between them is within the range of allowed<a name="line.262"></a>
<FONT color="green">263</FONT>         * error (inclusive).<a name="line.263"></a>
<FONT color="green">264</FONT>         *<a name="line.264"></a>
<FONT color="green">265</FONT>         * @param x First value.<a name="line.265"></a>
<FONT color="green">266</FONT>         * @param y Second value.<a name="line.266"></a>
<FONT color="green">267</FONT>         * @param eps Amount of allowed absolute error.<a name="line.267"></a>
<FONT color="green">268</FONT>         * @return {@code true} if the values are two adjacent floating point<a name="line.268"></a>
<FONT color="green">269</FONT>         * numbers or they are within range of each other.<a name="line.269"></a>
<FONT color="green">270</FONT>         */<a name="line.270"></a>
<FONT color="green">271</FONT>        public static boolean equals(double x, double y, double eps) {<a name="line.271"></a>
<FONT color="green">272</FONT>            return equals(x, y, 1) || FastMath.abs(y - x) &lt;= eps;<a name="line.272"></a>
<FONT color="green">273</FONT>        }<a name="line.273"></a>
<FONT color="green">274</FONT>    <a name="line.274"></a>
<FONT color="green">275</FONT>        /**<a name="line.275"></a>
<FONT color="green">276</FONT>         * Returns {@code true} if there is no double value strictly between the<a name="line.276"></a>
<FONT color="green">277</FONT>         * arguments or the reltaive difference between them is smaller or equal<a name="line.277"></a>
<FONT color="green">278</FONT>         * to the given tolerance.<a name="line.278"></a>
<FONT color="green">279</FONT>         *<a name="line.279"></a>
<FONT color="green">280</FONT>         * @param x First value.<a name="line.280"></a>
<FONT color="green">281</FONT>         * @param y Second value.<a name="line.281"></a>
<FONT color="green">282</FONT>         * @param eps Amount of allowed relative error.<a name="line.282"></a>
<FONT color="green">283</FONT>         * @return {@code true} if the values are two adjacent floating point<a name="line.283"></a>
<FONT color="green">284</FONT>         * numbers or they are within range of each other.<a name="line.284"></a>
<FONT color="green">285</FONT>         * @since 3.1<a name="line.285"></a>
<FONT color="green">286</FONT>         */<a name="line.286"></a>
<FONT color="green">287</FONT>        public static boolean equalsWithRelativeTolerance(double x, double y, double eps) {<a name="line.287"></a>
<FONT color="green">288</FONT>            if (equals(x, y, 1)) {<a name="line.288"></a>
<FONT color="green">289</FONT>                return true;<a name="line.289"></a>
<FONT color="green">290</FONT>            }<a name="line.290"></a>
<FONT color="green">291</FONT>    <a name="line.291"></a>
<FONT color="green">292</FONT>            final double absoluteMax = FastMath.max(FastMath.abs(x), FastMath.abs(y));<a name="line.292"></a>
<FONT color="green">293</FONT>            final double relativeDifference = FastMath.abs((x - y) / absoluteMax);<a name="line.293"></a>
<FONT color="green">294</FONT>    <a name="line.294"></a>
<FONT color="green">295</FONT>            return relativeDifference &lt;= eps;<a name="line.295"></a>
<FONT color="green">296</FONT>        }<a name="line.296"></a>
<FONT color="green">297</FONT>    <a name="line.297"></a>
<FONT color="green">298</FONT>        /**<a name="line.298"></a>
<FONT color="green">299</FONT>         * Returns true if both arguments are NaN or are equal or within the range<a name="line.299"></a>
<FONT color="green">300</FONT>         * of allowed error (inclusive).<a name="line.300"></a>
<FONT color="green">301</FONT>         *<a name="line.301"></a>
<FONT color="green">302</FONT>         * @param x first value<a name="line.302"></a>
<FONT color="green">303</FONT>         * @param y second value<a name="line.303"></a>
<FONT color="green">304</FONT>         * @param eps the amount of absolute error to allow.<a name="line.304"></a>
<FONT color="green">305</FONT>         * @return {@code true} if the values are equal or within range of each other,<a name="line.305"></a>
<FONT color="green">306</FONT>         * or both are NaN.<a name="line.306"></a>
<FONT color="green">307</FONT>         * @since 2.2<a name="line.307"></a>
<FONT color="green">308</FONT>         */<a name="line.308"></a>
<FONT color="green">309</FONT>        public static boolean equalsIncludingNaN(double x, double y, double eps) {<a name="line.309"></a>
<FONT color="green">310</FONT>            return equalsIncludingNaN(x, y) || (FastMath.abs(y - x) &lt;= eps);<a name="line.310"></a>
<FONT color="green">311</FONT>        }<a name="line.311"></a>
<FONT color="green">312</FONT>    <a name="line.312"></a>
<FONT color="green">313</FONT>        /**<a name="line.313"></a>
<FONT color="green">314</FONT>         * Returns true if both arguments are equal or within the range of allowed<a name="line.314"></a>
<FONT color="green">315</FONT>         * error (inclusive).<a name="line.315"></a>
<FONT color="green">316</FONT>         * Two float numbers are considered equal if there are {@code (maxUlps - 1)}<a name="line.316"></a>
<FONT color="green">317</FONT>         * (or fewer) floating point numbers between them, i.e. two adjacent floating<a name="line.317"></a>
<FONT color="green">318</FONT>         * point numbers are considered equal.<a name="line.318"></a>
<FONT color="green">319</FONT>         * Adapted from &lt;a<a name="line.319"></a>
<FONT color="green">320</FONT>         * href="http://www.cygnus-software.com/papers/comparingfloats/comparingfloats.htm"&gt;<a name="line.320"></a>
<FONT color="green">321</FONT>         * Bruce Dawson&lt;/a&gt;<a name="line.321"></a>
<FONT color="green">322</FONT>         *<a name="line.322"></a>
<FONT color="green">323</FONT>         * @param x first value<a name="line.323"></a>
<FONT color="green">324</FONT>         * @param y second value<a name="line.324"></a>
<FONT color="green">325</FONT>         * @param maxUlps {@code (maxUlps - 1)} is the number of floating point<a name="line.325"></a>
<FONT color="green">326</FONT>         * values between {@code x} and {@code y}.<a name="line.326"></a>
<FONT color="green">327</FONT>         * @return {@code true} if there are fewer than {@code maxUlps} floating<a name="line.327"></a>
<FONT color="green">328</FONT>         * point values between {@code x} and {@code y}.<a name="line.328"></a>
<FONT color="green">329</FONT>         */<a name="line.329"></a>
<FONT color="green">330</FONT>        public static boolean equals(double x, double y, int maxUlps) {<a name="line.330"></a>
<FONT color="green">331</FONT>            long xInt = Double.doubleToLongBits(x);<a name="line.331"></a>
<FONT color="green">332</FONT>            long yInt = Double.doubleToLongBits(y);<a name="line.332"></a>
<FONT color="green">333</FONT>    <a name="line.333"></a>
<FONT color="green">334</FONT>            // Make lexicographically ordered as a two's-complement integer.<a name="line.334"></a>
<FONT color="green">335</FONT>            if (xInt &lt; 0) {<a name="line.335"></a>
<FONT color="green">336</FONT>                xInt = SGN_MASK - xInt;<a name="line.336"></a>
<FONT color="green">337</FONT>            }<a name="line.337"></a>
<FONT color="green">338</FONT>            if (yInt &lt; 0) {<a name="line.338"></a>
<FONT color="green">339</FONT>                yInt = SGN_MASK - yInt;<a name="line.339"></a>
<FONT color="green">340</FONT>            }<a name="line.340"></a>
<FONT color="green">341</FONT>    <a name="line.341"></a>
<FONT color="green">342</FONT>            final boolean isEqual = FastMath.abs(xInt - yInt) &lt;= maxUlps;<a name="line.342"></a>
<FONT color="green">343</FONT>    <a name="line.343"></a>
<FONT color="green">344</FONT>            return isEqual &amp;&amp; !Double.isNaN(x) &amp;&amp; !Double.isNaN(y);<a name="line.344"></a>
<FONT color="green">345</FONT>        }<a name="line.345"></a>
<FONT color="green">346</FONT>    <a name="line.346"></a>
<FONT color="green">347</FONT>        /**<a name="line.347"></a>
<FONT color="green">348</FONT>         * Returns true if both arguments are NaN or if they are equal as defined<a name="line.348"></a>
<FONT color="green">349</FONT>         * by {@link #equals(double,double,int) equals(x, y, maxUlps)}.<a name="line.349"></a>
<FONT color="green">350</FONT>         *<a name="line.350"></a>
<FONT color="green">351</FONT>         * @param x first value<a name="line.351"></a>
<FONT color="green">352</FONT>         * @param y second value<a name="line.352"></a>
<FONT color="green">353</FONT>         * @param maxUlps {@code (maxUlps - 1)} is the number of floating point<a name="line.353"></a>
<FONT color="green">354</FONT>         * values between {@code x} and {@code y}.<a name="line.354"></a>
<FONT color="green">355</FONT>         * @return {@code true} if both arguments are NaN or if there are less than<a name="line.355"></a>
<FONT color="green">356</FONT>         * {@code maxUlps} floating point values between {@code x} and {@code y}.<a name="line.356"></a>
<FONT color="green">357</FONT>         * @since 2.2<a name="line.357"></a>
<FONT color="green">358</FONT>         */<a name="line.358"></a>
<FONT color="green">359</FONT>        public static boolean equalsIncludingNaN(double x, double y, int maxUlps) {<a name="line.359"></a>
<FONT color="green">360</FONT>            return (Double.isNaN(x) &amp;&amp; Double.isNaN(y)) || equals(x, y, maxUlps);<a name="line.360"></a>
<FONT color="green">361</FONT>        }<a name="line.361"></a>
<FONT color="green">362</FONT>    <a name="line.362"></a>
<FONT color="green">363</FONT>        /**<a name="line.363"></a>
<FONT color="green">364</FONT>         * Rounds the given value to the specified number of decimal places.<a name="line.364"></a>
<FONT color="green">365</FONT>         * The value is rounded using the {@link BigDecimal#ROUND_HALF_UP} method.<a name="line.365"></a>
<FONT color="green">366</FONT>         *<a name="line.366"></a>
<FONT color="green">367</FONT>         * @param x Value to round.<a name="line.367"></a>
<FONT color="green">368</FONT>         * @param scale Number of digits to the right of the decimal point.<a name="line.368"></a>
<FONT color="green">369</FONT>         * @return the rounded value.<a name="line.369"></a>
<FONT color="green">370</FONT>         * @since 1.1 (previously in {@code MathUtils}, moved as of version 3.0)<a name="line.370"></a>
<FONT color="green">371</FONT>         */<a name="line.371"></a>
<FONT color="green">372</FONT>        public static double round(double x, int scale) {<a name="line.372"></a>
<FONT color="green">373</FONT>            return round(x, scale, BigDecimal.ROUND_HALF_UP);<a name="line.373"></a>
<FONT color="green">374</FONT>        }<a name="line.374"></a>
<FONT color="green">375</FONT>    <a name="line.375"></a>
<FONT color="green">376</FONT>        /**<a name="line.376"></a>
<FONT color="green">377</FONT>         * Rounds the given value to the specified number of decimal places.<a name="line.377"></a>
<FONT color="green">378</FONT>         * The value is rounded using the given method which is any method defined<a name="line.378"></a>
<FONT color="green">379</FONT>         * in {@link BigDecimal}.<a name="line.379"></a>
<FONT color="green">380</FONT>         * If {@code x} is infinite or {@code NaN}, then the value of {@code x} is<a name="line.380"></a>
<FONT color="green">381</FONT>         * returned unchanged, regardless of the other parameters.<a name="line.381"></a>
<FONT color="green">382</FONT>         *<a name="line.382"></a>
<FONT color="green">383</FONT>         * @param x Value to round.<a name="line.383"></a>
<FONT color="green">384</FONT>         * @param scale Number of digits to the right of the decimal point.<a name="line.384"></a>
<FONT color="green">385</FONT>         * @param roundingMethod Rounding method as defined in {@link BigDecimal}.<a name="line.385"></a>
<FONT color="green">386</FONT>         * @return the rounded value.<a name="line.386"></a>
<FONT color="green">387</FONT>         * @throws ArithmeticException if {@code roundingMethod == ROUND_UNNECESSARY}<a name="line.387"></a>
<FONT color="green">388</FONT>         * and the specified scaling operation would require rounding.<a name="line.388"></a>
<FONT color="green">389</FONT>         * @throws IllegalArgumentException if {@code roundingMethod} does not<a name="line.389"></a>
<FONT color="green">390</FONT>         * represent a valid rounding mode.<a name="line.390"></a>
<FONT color="green">391</FONT>         * @since 1.1 (previously in {@code MathUtils}, moved as of version 3.0)<a name="line.391"></a>
<FONT color="green">392</FONT>         */<a name="line.392"></a>
<FONT color="green">393</FONT>        public static double round(double x, int scale, int roundingMethod) {<a name="line.393"></a>
<FONT color="green">394</FONT>            try {<a name="line.394"></a>
<FONT color="green">395</FONT>                return (new BigDecimal<a name="line.395"></a>
<FONT color="green">396</FONT>                       (Double.toString(x))<a name="line.396"></a>
<FONT color="green">397</FONT>                       .setScale(scale, roundingMethod))<a name="line.397"></a>
<FONT color="green">398</FONT>                       .doubleValue();<a name="line.398"></a>
<FONT color="green">399</FONT>            } catch (NumberFormatException ex) {<a name="line.399"></a>
<FONT color="green">400</FONT>                if (Double.isInfinite(x)) {<a name="line.400"></a>
<FONT color="green">401</FONT>                    return x;<a name="line.401"></a>
<FONT color="green">402</FONT>                } else {<a name="line.402"></a>
<FONT color="green">403</FONT>                    return Double.NaN;<a name="line.403"></a>
<FONT color="green">404</FONT>                }<a name="line.404"></a>
<FONT color="green">405</FONT>            }<a name="line.405"></a>
<FONT color="green">406</FONT>        }<a name="line.406"></a>
<FONT color="green">407</FONT>    <a name="line.407"></a>
<FONT color="green">408</FONT>        /**<a name="line.408"></a>
<FONT color="green">409</FONT>         * Rounds the given value to the specified number of decimal places.<a name="line.409"></a>
<FONT color="green">410</FONT>         * The value is rounded using the {@link BigDecimal#ROUND_HALF_UP} method.<a name="line.410"></a>
<FONT color="green">411</FONT>         *<a name="line.411"></a>
<FONT color="green">412</FONT>         * @param x Value to round.<a name="line.412"></a>
<FONT color="green">413</FONT>         * @param scale Number of digits to the right of the decimal point.<a name="line.413"></a>
<FONT color="green">414</FONT>         * @return the rounded value.<a name="line.414"></a>
<FONT color="green">415</FONT>         * @since 1.1 (previously in {@code MathUtils}, moved as of version 3.0)<a name="line.415"></a>
<FONT color="green">416</FONT>         */<a name="line.416"></a>
<FONT color="green">417</FONT>        public static float round(float x, int scale) {<a name="line.417"></a>
<FONT color="green">418</FONT>            return round(x, scale, BigDecimal.ROUND_HALF_UP);<a name="line.418"></a>
<FONT color="green">419</FONT>        }<a name="line.419"></a>
<FONT color="green">420</FONT>    <a name="line.420"></a>
<FONT color="green">421</FONT>        /**<a name="line.421"></a>
<FONT color="green">422</FONT>         * Rounds the given value to the specified number of decimal places.<a name="line.422"></a>
<FONT color="green">423</FONT>         * The value is rounded using the given method which is any method defined<a name="line.423"></a>
<FONT color="green">424</FONT>         * in {@link BigDecimal}.<a name="line.424"></a>
<FONT color="green">425</FONT>         *<a name="line.425"></a>
<FONT color="green">426</FONT>         * @param x Value to round.<a name="line.426"></a>
<FONT color="green">427</FONT>         * @param scale Number of digits to the right of the decimal point.<a name="line.427"></a>
<FONT color="green">428</FONT>         * @param roundingMethod Rounding method as defined in {@link BigDecimal}.<a name="line.428"></a>
<FONT color="green">429</FONT>         * @return the rounded value.<a name="line.429"></a>
<FONT color="green">430</FONT>         * @since 1.1 (previously in {@code MathUtils}, moved as of version 3.0)<a name="line.430"></a>
<FONT color="green">431</FONT>         * @throws MathArithmeticException if an exact operation is required but result is not exact<a name="line.431"></a>
<FONT color="green">432</FONT>         * @throws MathIllegalArgumentException if {@code roundingMethod} is not a valid rounding method.<a name="line.432"></a>
<FONT color="green">433</FONT>         */<a name="line.433"></a>
<FONT color="green">434</FONT>        public static float round(float x, int scale, int roundingMethod)<a name="line.434"></a>
<FONT color="green">435</FONT>            throws MathArithmeticException, MathIllegalArgumentException {<a name="line.435"></a>
<FONT color="green">436</FONT>            final float sign = FastMath.copySign(1f, x);<a name="line.436"></a>
<FONT color="green">437</FONT>            final float factor = (float) FastMath.pow(10.0f, scale) * sign;<a name="line.437"></a>
<FONT color="green">438</FONT>            return (float) roundUnscaled(x * factor, sign, roundingMethod) / factor;<a name="line.438"></a>
<FONT color="green">439</FONT>        }<a name="line.439"></a>
<FONT color="green">440</FONT>    <a name="line.440"></a>
<FONT color="green">441</FONT>        /**<a name="line.441"></a>
<FONT color="green">442</FONT>         * Rounds the given non-negative value to the "nearest" integer. Nearest is<a name="line.442"></a>
<FONT color="green">443</FONT>         * determined by the rounding method specified. Rounding methods are defined<a name="line.443"></a>
<FONT color="green">444</FONT>         * in {@link BigDecimal}.<a name="line.444"></a>
<FONT color="green">445</FONT>         *<a name="line.445"></a>
<FONT color="green">446</FONT>         * @param unscaled Value to round.<a name="line.446"></a>
<FONT color="green">447</FONT>         * @param sign Sign of the original, scaled value.<a name="line.447"></a>
<FONT color="green">448</FONT>         * @param roundingMethod Rounding method, as defined in {@link BigDecimal}.<a name="line.448"></a>
<FONT color="green">449</FONT>         * @return the rounded value.<a name="line.449"></a>
<FONT color="green">450</FONT>         * @throws MathArithmeticException if an exact operation is required but result is not exact<a name="line.450"></a>
<FONT color="green">451</FONT>         * @throws MathIllegalArgumentException if {@code roundingMethod} is not a valid rounding method.<a name="line.451"></a>
<FONT color="green">452</FONT>         * @since 1.1 (previously in {@code MathUtils}, moved as of version 3.0)<a name="line.452"></a>
<FONT color="green">453</FONT>         */<a name="line.453"></a>
<FONT color="green">454</FONT>        private static double roundUnscaled(double unscaled,<a name="line.454"></a>
<FONT color="green">455</FONT>                                            double sign,<a name="line.455"></a>
<FONT color="green">456</FONT>                                            int roundingMethod)<a name="line.456"></a>
<FONT color="green">457</FONT>            throws MathArithmeticException, MathIllegalArgumentException {<a name="line.457"></a>
<FONT color="green">458</FONT>            switch (roundingMethod) {<a name="line.458"></a>
<FONT color="green">459</FONT>            case BigDecimal.ROUND_CEILING :<a name="line.459"></a>
<FONT color="green">460</FONT>                if (sign == -1) {<a name="line.460"></a>
<FONT color="green">461</FONT>                    unscaled = FastMath.floor(FastMath.nextAfter(unscaled, Double.NEGATIVE_INFINITY));<a name="line.461"></a>
<FONT color="green">462</FONT>                } else {<a name="line.462"></a>
<FONT color="green">463</FONT>                    unscaled = FastMath.ceil(FastMath.nextAfter(unscaled, Double.POSITIVE_INFINITY));<a name="line.463"></a>
<FONT color="green">464</FONT>                }<a name="line.464"></a>
<FONT color="green">465</FONT>                break;<a name="line.465"></a>
<FONT color="green">466</FONT>            case BigDecimal.ROUND_DOWN :<a name="line.466"></a>
<FONT color="green">467</FONT>                unscaled = FastMath.floor(FastMath.nextAfter(unscaled, Double.NEGATIVE_INFINITY));<a name="line.467"></a>
<FONT color="green">468</FONT>                break;<a name="line.468"></a>
<FONT color="green">469</FONT>            case BigDecimal.ROUND_FLOOR :<a name="line.469"></a>
<FONT color="green">470</FONT>                if (sign == -1) {<a name="line.470"></a>
<FONT color="green">471</FONT>                    unscaled = FastMath.ceil(FastMath.nextAfter(unscaled, Double.POSITIVE_INFINITY));<a name="line.471"></a>
<FONT color="green">472</FONT>                } else {<a name="line.472"></a>
<FONT color="green">473</FONT>                    unscaled = FastMath.floor(FastMath.nextAfter(unscaled, Double.NEGATIVE_INFINITY));<a name="line.473"></a>
<FONT color="green">474</FONT>                }<a name="line.474"></a>
<FONT color="green">475</FONT>                break;<a name="line.475"></a>
<FONT color="green">476</FONT>            case BigDecimal.ROUND_HALF_DOWN : {<a name="line.476"></a>
<FONT color="green">477</FONT>                unscaled = FastMath.nextAfter(unscaled, Double.NEGATIVE_INFINITY);<a name="line.477"></a>
<FONT color="green">478</FONT>                double fraction = unscaled - FastMath.floor(unscaled);<a name="line.478"></a>
<FONT color="green">479</FONT>                if (fraction &gt; 0.5) {<a name="line.479"></a>
<FONT color="green">480</FONT>                    unscaled = FastMath.ceil(unscaled);<a name="line.480"></a>
<FONT color="green">481</FONT>                } else {<a name="line.481"></a>
<FONT color="green">482</FONT>                    unscaled = FastMath.floor(unscaled);<a name="line.482"></a>
<FONT color="green">483</FONT>                }<a name="line.483"></a>
<FONT color="green">484</FONT>                break;<a name="line.484"></a>
<FONT color="green">485</FONT>            }<a name="line.485"></a>
<FONT color="green">486</FONT>            case BigDecimal.ROUND_HALF_EVEN : {<a name="line.486"></a>
<FONT color="green">487</FONT>                double fraction = unscaled - FastMath.floor(unscaled);<a name="line.487"></a>
<FONT color="green">488</FONT>                if (fraction &gt; 0.5) {<a name="line.488"></a>
<FONT color="green">489</FONT>                    unscaled = FastMath.ceil(unscaled);<a name="line.489"></a>
<FONT color="green">490</FONT>                } else if (fraction &lt; 0.5) {<a name="line.490"></a>
<FONT color="green">491</FONT>                    unscaled = FastMath.floor(unscaled);<a name="line.491"></a>
<FONT color="green">492</FONT>                } else {<a name="line.492"></a>
<FONT color="green">493</FONT>                    // The following equality test is intentional and needed for rounding purposes<a name="line.493"></a>
<FONT color="green">494</FONT>                    if (FastMath.floor(unscaled) / 2.0 == FastMath.floor(Math<a name="line.494"></a>
<FONT color="green">495</FONT>                        .floor(unscaled) / 2.0)) { // even<a name="line.495"></a>
<FONT color="green">496</FONT>                        unscaled = FastMath.floor(unscaled);<a name="line.496"></a>
<FONT color="green">497</FONT>                    } else { // odd<a name="line.497"></a>
<FONT color="green">498</FONT>                        unscaled = FastMath.ceil(unscaled);<a name="line.498"></a>
<FONT color="green">499</FONT>                    }<a name="line.499"></a>
<FONT color="green">500</FONT>                }<a name="line.500"></a>
<FONT color="green">501</FONT>                break;<a name="line.501"></a>
<FONT color="green">502</FONT>            }<a name="line.502"></a>
<FONT color="green">503</FONT>            case BigDecimal.ROUND_HALF_UP : {<a name="line.503"></a>
<FONT color="green">504</FONT>                unscaled = FastMath.nextAfter(unscaled, Double.POSITIVE_INFINITY);<a name="line.504"></a>
<FONT color="green">505</FONT>                double fraction = unscaled - FastMath.floor(unscaled);<a name="line.505"></a>
<FONT color="green">506</FONT>                if (fraction &gt;= 0.5) {<a name="line.506"></a>
<FONT color="green">507</FONT>                    unscaled = FastMath.ceil(unscaled);<a name="line.507"></a>
<FONT color="green">508</FONT>                } else {<a name="line.508"></a>
<FONT color="green">509</FONT>                    unscaled = FastMath.floor(unscaled);<a name="line.509"></a>
<FONT color="green">510</FONT>                }<a name="line.510"></a>
<FONT color="green">511</FONT>                break;<a name="line.511"></a>
<FONT color="green">512</FONT>            }<a name="line.512"></a>
<FONT color="green">513</FONT>            case BigDecimal.ROUND_UNNECESSARY :<a name="line.513"></a>
<FONT color="green">514</FONT>                if (unscaled != FastMath.floor(unscaled)) {<a name="line.514"></a>
<FONT color="green">515</FONT>                    throw new MathArithmeticException();<a name="line.515"></a>
<FONT color="green">516</FONT>                }<a name="line.516"></a>
<FONT color="green">517</FONT>                break;<a name="line.517"></a>
<FONT color="green">518</FONT>            case BigDecimal.ROUND_UP :<a name="line.518"></a>
<FONT color="green">519</FONT>                unscaled = FastMath.ceil(FastMath.nextAfter(unscaled,  Double.POSITIVE_INFINITY));<a name="line.519"></a>
<FONT color="green">520</FONT>                break;<a name="line.520"></a>
<FONT color="green">521</FONT>            default :<a name="line.521"></a>
<FONT color="green">522</FONT>                throw new MathIllegalArgumentException(LocalizedFormats.INVALID_ROUNDING_METHOD,<a name="line.522"></a>
<FONT color="green">523</FONT>                                                       roundingMethod,<a name="line.523"></a>
<FONT color="green">524</FONT>                                                       "ROUND_CEILING", BigDecimal.ROUND_CEILING,<a name="line.524"></a>
<FONT color="green">525</FONT>                                                       "ROUND_DOWN", BigDecimal.ROUND_DOWN,<a name="line.525"></a>
<FONT color="green">526</FONT>                                                       "ROUND_FLOOR", BigDecimal.ROUND_FLOOR,<a name="line.526"></a>
<FONT color="green">527</FONT>                                                       "ROUND_HALF_DOWN", BigDecimal.ROUND_HALF_DOWN,<a name="line.527"></a>
<FONT color="green">528</FONT>                                                       "ROUND_HALF_EVEN", BigDecimal.ROUND_HALF_EVEN,<a name="line.528"></a>
<FONT color="green">529</FONT>                                                       "ROUND_HALF_UP", BigDecimal.ROUND_HALF_UP,<a name="line.529"></a>
<FONT color="green">530</FONT>                                                       "ROUND_UNNECESSARY", BigDecimal.ROUND_UNNECESSARY,<a name="line.530"></a>
<FONT color="green">531</FONT>                                                       "ROUND_UP", BigDecimal.ROUND_UP);<a name="line.531"></a>
<FONT color="green">532</FONT>            }<a name="line.532"></a>
<FONT color="green">533</FONT>            return unscaled;<a name="line.533"></a>
<FONT color="green">534</FONT>        }<a name="line.534"></a>
<FONT color="green">535</FONT>    <a name="line.535"></a>
<FONT color="green">536</FONT>    <a name="line.536"></a>
<FONT color="green">537</FONT>        /**<a name="line.537"></a>
<FONT color="green">538</FONT>         * Computes a number {@code delta} close to {@code originalDelta} with<a name="line.538"></a>
<FONT color="green">539</FONT>         * the property that &lt;pre&gt;&lt;code&gt;<a name="line.539"></a>
<FONT color="green">540</FONT>         *   x + delta - x<a name="line.540"></a>
<FONT color="green">541</FONT>         * &lt;/code&gt;&lt;/pre&gt;<a name="line.541"></a>
<FONT color="green">542</FONT>         * is exactly machine-representable.<a name="line.542"></a>
<FONT color="green">543</FONT>         * This is useful when computing numerical derivatives, in order to reduce<a name="line.543"></a>
<FONT color="green">544</FONT>         * roundoff errors.<a name="line.544"></a>
<FONT color="green">545</FONT>         *<a name="line.545"></a>
<FONT color="green">546</FONT>         * @param x Value.<a name="line.546"></a>
<FONT color="green">547</FONT>         * @param originalDelta Offset value.<a name="line.547"></a>
<FONT color="green">548</FONT>         * @return a number {@code delta} so that {@code x + delta} and {@code x}<a name="line.548"></a>
<FONT color="green">549</FONT>         * differ by a representable floating number.<a name="line.549"></a>
<FONT color="green">550</FONT>         */<a name="line.550"></a>
<FONT color="green">551</FONT>        public static double representableDelta(double x,<a name="line.551"></a>
<FONT color="green">552</FONT>                                                double originalDelta) {<a name="line.552"></a>
<FONT color="green">553</FONT>            return x + originalDelta - x;<a name="line.553"></a>
<FONT color="green">554</FONT>        }<a name="line.554"></a>
<FONT color="green">555</FONT>    }<a name="line.555"></a>




























































</PRE>
</BODY>
</HTML>
